A possible swap of Jarrett Jack (top right) and Marcus Thornton (bottom right) by the Cavaliers and Nets could then lead Cleveland to try to shed Thornton's contract to make room for superstar free agent LeBron James (left). Photo: NBAE via Getty Images (3)

ORLANDO, Fla. — Despite being far over the salary cap, the Nets could still play a role in the LeBron James sweepstakes.

No, not because the Nets are going to get the league’s best player to sign either for the league minimum or the mini mid-level exception, but because they could help James’ old team carve out enough cap room to sign him to a maximum contract.

Yahoo! Sports reported late Sunday a Nets trade of Marcus Thornton to the Cavaliers for Jarrett Jack — a deal that has been rumored to be on the verge of happening for a couple of weeks — might need to expand to a third team. The Cavaliers would like to flip Thornton’s $8.5 million expiring contract in order to open up enough cap room to sign James to a max contract if he chooses to go back to Cleveland this summer.

For the Nets, getting Jack would give them a backup point guard to play behind Deron Williams — something they need after Shaun Livingston went to the Warriors in free agency last week. Jack also would be able to play alongside Williams as Livingston did so effectively for the Nets last season if new coach Lionel Hollins chooses to do so.

The Nets could then move on to fill the hole vacated by Thornton’s departure for a bench scorer on the wings with 2011 second-round pick Bojan Bogdanovic, who league sources confirmed to The Post is in discussions about coming to the NBA next season for the mini mid-level.

Bojan BogdanovicPhoto: Jeff Zelevansky

Bogdanovic, 25, averaged 14.8 points in Euroleague play this season for Turkish power Fenerbahce Ulker, and at 6-foot-8 would give the Nets another young option on the wing who is also a capable 3-point shooter. He also is expected to play for Croatia in the FIBA World Cup of Basketball in Spain later this summer.

Entering free agency, the Nets had earmarked the exception to use on Livingston, who general manager Billy King called the team’s “number one priority” during the season after he stepped into the backcourt and played extremely well alongside Williams.

But once Livingston quickly went off the market, Bogdanovic became the next and most obvious option for the Nets to use the exception on. He would present a move towards getting younger and they could lock him into a reasonable contract of three years for roughly $10 million.

NTV Spor in Turkey first reported Bogdanovic and the Nets were in discussions.

The Nets dropped to 1-1 in summer league play Sunday by losing 110-91 to the Heat. Former UConn star Shabazz Napier, Miami’s first-round pick, had 17 points for the Heat, while Mason Plumlee had 18 points to lead the Nets, who will introduce Hollins at a press conference Monday morning at Barclays Center.

While the Nets have yet to announce who will be part of Hollins’ coaching staff, one likely option will be Henry Bibby, a longtime Hollins assistant in Memphis who spent last season working under Maurice Cheeks with the Pistons.

Other names that have been reported as possibilities for Hollins’ staff include former Suns, Sonics and Kings coach Paul Westphal, Lakers assistant Johnny Davis — a teammate of Hollins on the 1977 champion Trail Blazers and a former assistant on his staff in Memphis — and current Nets assistant Joe Prunty.